X+44/2x.X=11

Solution for X+44/2x.X=11 equation:

X+44/2X.X=11

We move all terms to the left:

X+44/2X.X-(11)=0


Domain of the equation: 2X.X!=0

X!=0/1

X!=0

X∈R


We multiply all the terms by the denominator


X*2X.X-11*2X.X+44=0

Wy multiply elements

2X^2-22X+44=0

a = 2; b = -22; c = +44;
Δ = b2-4ac
Δ = -222-4·2·44
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{33}}{2*2}=\frac{22-2\sqrt{33}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{33}}{2*2}=\frac{22+2\sqrt{33}}{4}
$